A Probability Question.

[JohnHarris]

You are taking a test where the final score is the number right minus the number wrong and the higher the score the better. If you think the answer is choice (a) with a certainty of x%, what should you do. That is relative to the value of x, should you not answer the question (0 points) or give (a) as the answer to the question (you expect y point on average where y is non-negative).

HINT: Taking the test 'a number of times' you would expect to get the answer right N times depending on x and the answer wrong M times depending on the value of x, so the average number of points you would get is
(N-M)/(N+M).

SOURCE: Me, the devilishly cleaver something or another.

[JohnHarris]

Oh well, no one appears interested so I'll just answer it myself. The expected number of points per problem you are unsure of is 2x-1. This says if you are 100% sure (x=1) you will expect to get a point and if you are 0% sure (x=0) you will expect to lose a point. If you are less than 50 percent sure you would expect to lose at least part of a point.

For test purposes this says you will get a better score if you are pretty sure (more than 50% sure) of the answer and go ahead and 'guess'. So tentatively mark an answer if you are pretty sure, i.e. put a check mark by the problem or keep track of the problems some way. If you have time, go back and work on them. If not, just let them stand

If the number of points you get on the test is just the number correct then always guess at an answer. So if you are running out of time and can't do another problem, just go back and answer all the skipped question as choice (a) or whatever.

[tim]

Totally unrelated to the GMAT, both in terms of math content and test taking strategy, but what you’ve written is indeed correct..